# Hoffman Criterion

The resulting failure index in Hoffman’s theory for an orthotropic lamina in a general state of plane stress (2D) with unequal tensile and compressive strengths is given by:

${F}_{index}=\left(\frac{1}{{X}_{T}}-\frac{1}{{X}_{C}}\right){\text{σ}}_{1}+\left(\frac{1}{{Y}_{T}}-\frac{1}{{Y}_{C}}\right){\text{σ}}_{2}+\frac{{\text{σ}}_{1}^{2}}{{X}_{T}{X}_{C}}+\frac{{\text{σ}}_{2}^{2}}{{Y}_{T}{Y}_{C}}-\frac{{\text{σ}}_{1}{\text{σ}}_{2}}{{X}_{T}{X}_{C}}+\frac{{\text{τ}}_{12}^{2}}{{S}^{2}}$

Where:
• $Xt,Xc$ are the maximum allowable stresses in the 1-direction in tension and compression,
• $Yt,Yc$ are the maximum allowable stresses in the 2-direction in tension and compression,
• $S$ is the allowable in-plane shear stress

## Syntax

HoffmanFT(tensor,xt,xc,yt,yc,s,sets,plies,elems,parts,props,pool_name,layer_index,opt_str)

## Arguments

tensor
Stress table
xt
Allowable tensile stress in ply material direction 1
xc
Allowable compressive stress in ply material direction 1
yt
Allowable tensile stress in ply material direction 2
yc
Allowable compressive stress in ply material direction 2
s
Allowable in-plane shear stress
sets
Set table (D=NULL)
plies
Ply table (D=NULL)
elems
Element table (D)
parts
Part table (D)
props
Property table (D)
pool_name
Pool name (D=@current_pool)
layer_index
Layer index (D=@current_slice_index)
opt_str
This is an optional argument, which can passed if needed (D=option).